A MODEL OF THE CONSUMPTION RESPONSE TO FISCAL STIMULUS PAYMENTS
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Econometrica, Vol. 82, No. 4 (July, 2014), 1199–1239
A MODEL OF THE CONSUMPTION RESPONSE TO FISCAL
STIMULUS PAYMENTS
BY GREG KAPLAN AND GIOVANNI L. VIOLANTE1
A wide body of empirical evidence finds that approximately 25 percent of fiscal stim-
ulus payments (e.g., tax rebates) are spent on nondurable household consumption in
the quarter that they are received. To interpret this fact, we develop a structural eco-
nomic model where households can hold two assets: a low-return liquid asset (e.g., cash,
checking account) and a high-return illiquid asset that carries a transaction cost (e.g.,
housing, retirement account). The optimal life-cycle pattern of portfolio choice implies
that many households in the model are “wealthy hand-to-mouth”: they hold little or no
liquid wealth despite owning sizable quantities of illiquid assets. Therefore, they display
large propensities to consume out of additional transitory income, and small propensi-
ties to consume out of news about future income. We document the existence of such
households in data from the Survey of Consumer Finances. A version of the model
parameterized to the 2001 tax rebate episode yields consumption responses to fiscal
stimulus payments that are in line with the evidence, and an order of magnitude larger
than in the standard “one-asset” framework. The model’s nonlinearities with respect to
the rebate size and the prevailing aggregate economic conditions have implications for
policy design.
KEYWORDS: Consumption, fiscal stimulus payments, hand-to-mouth, liquidity.
1. INTRODUCTION
FISCAL STIMULUS PAYMENTS, such as transfers to households in the form of tax
rebates, are frequently used by governments to alleviate the impact of reces-
sions on households’ welfare. This type of fiscal intervention was authorized by
the U.S. Congress in the last two downturns of 2001 and 2007–2009.2 House-
holds received one-off payments that ranged from $500 to $1,000, depending
on the specific episode. In the aggregate, these fiscal outlays amounted to $38
billion in 2001 and $96 billion in 2008, roughly equivalent to 0.4–0.7% of an-
nual GDP.
On the empirical side, substantial progress has been made in measuring
the size of household consumption responses to the tax rebate episodes of
2001 and 2008. In both instances, the U.S. Treasury scheduled payments based
on the last two digits of individual Social Security Numbers, which are effec-
tively random. Johnson, Parker, and Souleles (2006, hereafter JPS) and Parker,
1
We thank Kurt Mitman for outstanding research assistance. We are grateful to Jonathan
Heathcote, Ricardo Lagos, Sydney Ludvigson, and Sam Schulhofer-Wohl for their useful insights,
to numerous seminar participants for comments, and to Jonathan Parker and Lubos Pastor for
sharing their data. This research is supported by Grant 1127632 from the National Science Foun-
dation.
2
In the context of the latest downturn, Oh and Reis (2012) documented that the large fiscal ex-
pansion of 2007–2009 consisted primarily of growing social assistance, as opposed to government
purchases. Half of this expansion comprised discretionary fiscal stimulus transfers.
© 2014 The Econometric Society DOI: 10.3982/ECTA105281200 G. KAPLAN AND G. L. VIOLANTE
Souleles, Johnson, and McClelland (2011, hereafter PSJM) cleverly exploited
this randomized timing of the receipt of payments to estimate the effects of the
fiscal stimulus on consumption expenditures. Subsequently, Misra and Surico
(2013) refined the econometric analysis in these studies. Shapiro and Slem-
rod (2003a, 2003b, 2009) reinforced this evidence with informative qualitative
surveys on how consumers use their rebate.
This collective evidence convincingly concludes that households spend ap-
proximately 25 percent of rebates on nondurables in the quarter that they are
received. This strong consumption response is measured relative to the control
group of households (comparable, because of the randomization) that do not
receive the rebate in that same quarter. In the paper, we call this magnitude
the rebate coefficient.3
In spite of this large body of empirical research, there are no quantitative
studies of these episodes within dynamic structural models of household be-
havior. This gap in the literature is troubling because a thorough understand-
ing of the effectiveness of tax rebates as a short-term stimulus for aggregate
consumption is paramount for macroeconomists and policy makers.4 Identify-
ing the determinants of how consumers respond to stimulus payments helps
in choosing policy options and in assessing whether the same fiscal instrument
can be expected to be more or less effective under different macroeconomic
conditions.5
To develop a structural model that has some hope of matching this micro
evidence, one cannot rely on off-the-shelf consumption theory: the rational
expectations, life-cycle, buffer-stock model with one risk-free asset (Deaton
(1991), Carroll (1992, 1997), Ríos-Rull (1995), Huggett (1996); for a survey,
see Heathcote, Storesletten, and Violante (2009)) predicts that the marginal
propensity to consume (MPC) out of transitory income fluctuations, such as
tax rebates, should be negligible in the aggregate. In this standard one-asset
model, the only agents whose consumption would react significantly to receiv-
ing a rebate check are those who are constrained. However, under parameter-
izations where the model’s distribution of net worth is in line with the data,
3
In a regression where the dependent variable is household consumption growth in a given
quarter and the right-hand side variable is the size of the rebate received in that quarter, possi-
bly zero, the rebate coefficient measures the differential consumption growth of the treatment
group—the rebate recipients—relative to the control group of non-recipients.
4
Estimates by JPS (2006) feature prominently in the reports prepared by the Congressional
Budget Office (CBO (2009)) and the Council of Economic Advisors (CEA (2010)) documenting
and forecasting the macroeconomic effects of fiscal stimulus.
5
JPS (2006, p. 1607) ended their empirical analysis of the 2001 tax rebates with: “without know-
ing the full structural model underlying these results, we cannot conclude that future tax rebates will
necessarily have the same effect.” Shapiro and Slemrod (2003a, p. 394) ended theirs with “key pa-
rameters such as the propensity to consume are contingent on aggregate conditions in ways that are
difficult to anticipate.”CONSUMPTION RESPONSE TO FISCAL STIMULUS PAYMENTS 1201
the fraction of constrained households (usually around 10%) is too small to
generate a big enough response in the aggregate.6
We overcome this challenge by proposing a quantitative framework that
speaks to the data on both liquid and illiquid wealth, rather than on net worth
alone. To do this, we integrate the classic Baumol–Tobin model of money de-
mand into a partial-equilibrium version of the workhorse incomplete-markets
life-cycle economy. In our model, households can store wealth in two types of
instruments: a liquid asset, such as cash or bank accounts, and an illiquid as-
set, such as housing or retirement wealth. Households can also borrow through
unsecured credit. The trade-off between the liquid and illiquid asset is that the
latter earns an exogenously higher rate of return, but can be accessed only by
paying a transaction cost. The model is parameterized to replicate a number
of macroeconomic, life-cycle, and cross-sectional targets.
Besides the usual small fraction of poor hand-to-mouth agents with zero net
worth, our model features a significant number of what we call wealthy hand-
to-mouth households. These are households that hold sizable amounts of illiq-
uid wealth, yet optimally choose to consume all of their disposable income
during a pay-period. Examining asset portfolio and income data from the 2001
Survey of Consumer Finances through the lens of our two-asset model reveals
that roughly 1/3 of U.S. households fit this profile. Although in our model
these households act as if they are constrained, they would not appear con-
strained from the viewpoint of the one-asset model since they own substantial
net worth.
Why would households with sizable net worth optimally choose to consume
all of their randomly fluctuating earnings every period, instead of maintaining a
smooth consumption profile? The answer is that such households are better off
bearing the welfare loss rather than smoothing shocks because the latter option
entails either frequently paying the transaction cost to tap into their illiquid
asset, or holding large balances of cash and foregoing the high return on the
illiquid asset, or obtaining credit at expensive interest rates. This explanation is
reminiscent of calculations by Cochrane (1989) and, more recently, Browning
and Crossley (2001) showing that in some contexts the utility loss from setting
consumption equal to income, instead of fully optimizing, is second order.7
These wealthy hand-to-mouth households are the reason why our model can
generate strong aggregate consumption responses to fiscal stimulus payments:
6
Even the one-asset model can, under parameterizations where many agents hold close to
zero net worth and are very often constrained, predict nontrivial consumption responses. This
explains, for example, the sizable MPC out of lump-sum tax cuts reported in some of Heathcote’s
(2005) experiments aimed at quantifying deviations from Ricardian neutrality in this class of
economies.
7
The model by Campbell and Hercowitz (2009) also generates wealthy constrained agents
endogenously, but through a different mechanism from ours: periodically, households discover
they will have a special consumption need T periods ahead (e.g., the education of their kids). This
induces them to consume low amounts until they have saved enough for the special consumption
need.1202 G. KAPLAN AND G. L. VIOLANTE such households do not respond to the news of the rebate and have a high MPC when they receive their payment. When we replicate, by simulation, the randomized experiment associated with the tax rebate of 2001 within our struc- tural model, we find rebate coefficients between 11% and 25%, depending on the assumed information structure. Values at the low end of this range are obtained under the assumption that every household is fully aware of the pol- icy one quarter ahead. In this scenario, all the non hand-to-mouth households have already responded to the news when the rebate reaches their pockets, which reduces the effect of the policy at the time of receipt of the checks. Val- ues at the high end correspond to the case where all households are surprised by the payment when they receive it. We set our baseline between these two extremes, where half of households expect the check from the government and half are surprised by it, and obtain values near to 15%, that is, almost two- thirds of our preferred estimates of rebate coefficients in the micro data.8 The presence of wealthy hand-to-mouth households is also the crucial source of amplification relative to a plausibly calibrated one-asset model economy where rebate coefficients from model-simulated data are less than 1%. This pronounced magnification works through both the extensive and the inten- sive margin. First, in our two-asset model there are many more hand-to-mouth consumers, consistent with the SCF data. Second, the wealthy hand-to-mouth display larger MPCs out of tax rebates than their poor counterparts since they have higher wealth (tied up in the illiquid asset) and, therefore, higher desired target consumption. Several key implications of the model are in agreement with the data. Misra and Surico (2011) estimated the entire empirical distribution of consumption responses for 2001 and documented substantial heterogeneity: half of the pop- ulation displays no response at all and one-fifth display responses over 50%. They also uncovered high income households at both ends of the distribution. Our model replicates these two findings for two reasons. First, most of the model agents behave as PIH consumers and have MPCs close to zero, but the wealthy hand-to-mouth have MPCs close to 50%. Second, there are many high- income households among the wealthy hand-to-mouth. Moreover, the model implies a tight negative correlation between the size of the consumption re- sponse and the ratio of holdings of liquid wealth to income, as documented, for example, in Souleles (1999) or Broda and Parker (2012). Finally, the model features a marked size-asymmetry in the consumption responses to small and large payments (Hsieh (2003)): large rebates trigger many households to pay the transaction cost and deposit the extra income into the illiquid account, but when they adjust, these households are unconstrained and therefore save the bulk of their rebate. 8 In line with this intermediate scenario, for the 2008 episode, Broda and Parker (2012) docu- mented that roughly 60% of households learned about the policy in the quarter before Treasury began disbursing payments.
CONSUMPTION RESPONSE TO FISCAL STIMULUS PAYMENTS 1203 In a series of experiments, we use the structural model to demonstrate two useful lessons for policy design. First, the aggregate macroeconomic conditions surrounding the policy affect the rebate fraction consumed by households in nontrivial ways. In a mild recession, where income drops are small and short- lived, it is not worthwhile for the wealthy hand-to-mouth households to pay the transaction cost to access some of their illiquid assets (or to use expensive credit) in order to smooth consumption. As a result, liquidity constraints get amplified, and the aggregate consumption response to a fiscal stimulus pay- ment is strong. Conversely, at the outset of a severe recession that induces a large and long-lasting fall in income, many wealthy hand-to-mouth house- holds will choose to borrow or tap into their illiquid account to create a buffer of liquid assets that can be used to smooth consumption. As a result, fewer households are hand-to-mouth when the rebate is received. Thus, the effect of the stimulus on consumption is lower compared to when the same policy is implemented in a mild downturn. Second, we compare budget-equivalent policies with various degrees of phasing-out and show that, to achieve the strongest bang for the buck, the re- bate should be phased out around median income. A more targeted rebate has smaller effects because its size becomes large enough for the size-asymmetry to kick in, and because it misses many middle class wealthy hand-to-mouth households with high MPCs. The structural model is also useful to understand when the micro estimates of the rebate coefficients are quantitatively close to what they aim to mea- sure, that is, the average MPC out of the fiscal stimulus receipt. Recall that identification of the micro estimates comes from the randomized timing of the payments across households. As a result, the consumption response of the treatment group—the group that receives the check in a given week—is mea- sured relative to a control group that is composed of (i) households who are aware of the policy, but will receive the check in a later week, and (ii) house- holds who have already received the payment in a previous week. Thus, the control group’s response, which ideally should be unaffected by the policy, is generally a mix of the MPC out of the news about the payment, and the lagged MPC out of the payment. We explain that (i) the lag between the date when the policy enters agents’ information sets and the date when the transfer en- ters agents’ budget constraints and (ii) the exact specification of the regression, jointly determine whether the empirical estimate is biased. Independently of the regression results, our structural model implies that the average quarterly MPC out of a surprise fiscal stimulus receipt is 20%. For an anticipated stimu- lus payment, the MPC out of the receipt of the payment is 6%, and the MPC out of the news of the payment is 7%. Our model is related to four strands of literature. A pair of influential pa- pers by Campbell and Mankiw (1989, 1991) showed that some key aspects of the comovement of aggregate consumption, income, and interest rates are best viewed as generated not by a single forward-looking type of consumer, but
1204 G. KAPLAN AND G. L. VIOLANTE
rather by the coexistence of two types: one forward-looking and consuming its
permanent income (the saver); the other, highly impatient and following the
rule of thumb of spending its current income (the spender).9 Our model can
be seen as a microfoundation for this spender-saver view because, alongside
standard buffer-stock consumers, it endogenously generates hand-to-mouth
households. However, most households in this class are patient and own sub-
stantial illiquid assets, which critically changes some of the macroeconomic
implications of the model. We return to this point in the Conclusions.
The closest forebears to our framework are Angeletos, Laibson, Repetto,
Tobacman, and Weinberg (2001) and Laibson, Repetto, and Tobacman (2003).
These two studies quantitatively compared the life-cycle portfolio allocation
properties of two types of consumers: one with quasi-hyperbolic discounting
and one with geometric discounting. Relative to the model with standard pref-
erences, with quasi-hyperbolic consumers it is easier to generate both sizeable
borrowing through unsecured credit (since credit provides funding for instant
gratification) and saving predominantly in illiquid assets (since illiquidity pro-
tects quasi-hyperbolic agents from future consumption splurges). As a result,
the MPC out of predictable income changes can be large.10 Our exploration
of the two-asset model sheds some new light on its mechanisms and quanti-
tative reach. We demonstrate that, even when this environment is populated
by geometric consumers, it can yield large MPCs out of small transitory in-
come changes as long as it features enough wealthy hand-to-mouth house-
holds. Hyperbolic discounting magnifies the key economic forces behind the
strong (weak) demand for illiquid (liquid) assets, but it is not strictly necessary
to obtain a significant amplification relative to the one-asset environment. We
explain how to use cross-sectional data on household portfolios to measure
such households and, therefore, discipline the model’s parameterization. We
apply the framework to quantitatively analyze a relevant policy question that
has so far not been addressed through structural modeling.
Although in our model households ride out small shocks, they withdraw from
the illiquid account to smooth out large falls in income. This rich adjustment
pattern resembles that described by Chetty and Szeidl (2007) in a theoretical
model with ex ante consumption commitments, where the burden of moderate
income shocks is only absorbed by fluctuations in the “flexible” consumption
good, whereas large shocks also induce ex post changes in the “commitment”
good. Our model, where the illiquid asset (e.g., its housing component) gen-
9
Recent examples of this model are Galí, López-Salido, and Vallés (2007) and Justiniano,
Primiceri, and Tambalotti (2013).
10
Another framework that has the ability to generate a large MPC from windfall income is
the “rational inattention” model (Reis (2006)). However, without the addition of some form of
transaction cost—or a mechanism to generate enough wealthy hand-to-mouth consumers—this
framework cannot display small consumption responses to news about future payments, which is
a necessary condition to match the size of estimated rebate coefficients.CONSUMPTION RESPONSE TO FISCAL STIMULUS PAYMENTS 1205
erates a consumption flow, features a similar source of excess sensitivity in
nondurable consumption.
Finally, a number of papers embed the Baumol–Tobin insight—the presence
of a frictional transaction technology—into portfolio choice models. Promi-
nent recent examples are Alvarez, Atkeson, and Kehoe (2002), Alvarez and
Lippi (2009), Abel, Eberly, and Panageas (2009), and Alvarez, Guiso, and
Lippi (2012). Although our model is less analytically tractable than most of
this literature, it contains a number of additional features crucial for generat-
ing wealthy hand-to-mouth households and empirically plausible rebate coef-
ficients: endogenous nondurable consumption choices, borrowing constraints,
uninsurable risk in non-financial income, and a life-cycle saving motive. Some
examples of richer frameworks for quantitative analysis exist, but applications
are essentially limited to financial issues and monetary policy.11 Our exercise
shows that this is also a natural environment to quantitatively analyze fiscal
policy.
The rest of the paper proceeds as follows. In Section 2, we describe the 2001
tax rebate episode and present the associated empirical evidence on the es-
timated consumption responses. In Section 3, we outline our model, and in
Section 4, we document the presence of wealthy hand-to-mouth consumers in
the model and in the data. Section 5 describes our parameterization. Section 6
contains the quantitative analysis of the 2001 tax rebate in the structural model.
In Sections 7 and 8, we use the model to perform a number of experiments that
are useful to inform the design of policy. Section 9 concludes.
2. SUMMARY AND INTERPRETATION OF THE EMPIRICAL EVIDENCE
ON THE 2001 TAX REBATE
Background. The tax rebate of 2001 was part of a broader tax reform, the
Economic Growth and Tax Relief Reconciliation Act (EGTRRA), enacted in
May 2001 by the U.S. Congress. The reform included a reduction in the federal
personal income tax rate for the lowest bracket (the first $12,000 of earnings
for a married couple filing jointly and the first $6,000 for singles) from 15% to
10%, effective retroactively to January 2001. In order to make this component
of the reform highly visible during calendar year 2001, the Administration paid
11
For example, within incomplete-markets economies, Aiyagari and Gertler (1991) focused on
the equity premium; Erosa and Ventura (2002) revisited, quantitatively, the question of welfare
effects of inflation; Ragot (2011) studied the joint distribution of money and financial assets.
Two recent papers examined whether the existence of two assets featuring different return and
liquidity characteristics induces “excess sensitivity” in consumption. In Li (2009), a large MPC
out of anticipated income changes was obtained only for calibrations where households hold as
little as one-twentieth as much wealth as in the data. Huntley and Michelangeli’s (2014) model
focused exclusively on the distinction between taxable and tax-deferred assets. As a result, the
amplification in the MPC is very modest (2–4 percentage points) relative to the benchmark one-
asset model.1206 G. KAPLAN AND G. L. VIOLANTE
an advance refund to taxpayers, informally called a tax rebate, for money they
would have received from the Treasury only upon filing their tax returns in
April 2002. The vast majority of the rebate checks were mailed between the
end of July and the end of September 2001, in a sequence based on the last
two digits of the social security number (SSN). This sequence featured in the
news in June. At the same time, the Treasury mailed every taxpayer a letter
informing them in which week they would receive their check. The Treasury
calculated that checks were sent out to 92 million taxpayers, with almost 80
percent of them paying the maximum amount ($600, or 5% of $12,000, for
married couples), corresponding to a total outlay of $38B, or almost 0.4% of
2001 GDP.
From the point of view of economic theory, the tax rebate of 2001 has three
salient characteristics: (i) it is essentially a lump sum, since almost every house-
hold received $300 per adult; (ii) it is anticipated, at least for that part of the
population which received the check later and that, presumably, had enough
time to learn about the rebate either from the news, from the Treasury letter,
or from friends/family who had already collected theirs; and (iii) the timing of
receipt of the rebate has the feature of a randomized experiment because the
last two digits of a SSN are uncorrelated with any individual characteristics.
Empirical Evidence. JPS (2006) added a special module of questions to the
Consumer Expenditure Survey (CEX) that asks households about the timing
and amount of their rebate check. Among the various specifications estimated
by JPS (2006) to assess the impact of the rebate on consumption expenditures,
we will focus on their baseline:
(1) Δcit = β0s months + β1 Xit−1 + β2 Rit + εit
s
where Δcit is the change in nondurable expenditures of household i in quarter
t, months is a time dummy, Xit−1 is a vector of demographics, and Rit is the
dollar value of the rebate received by household i in quarter t. The coefficient
β2 , which we label the rebate coefficient, is the object of interest. Identification
of β2 comes from randomization in the timing of the receipt of rebate checks
across households. Since the size of the rebate is potentially endogenous, JPS
(2006) estimated equation (1) by 2SLS using, as an instrument, an indicator for
whether the rebate was received. Their key finding, reproduced in Table I, is
that β2 is estimated to be 0.37 for nondurable consumption. Since the original
estimates of JPS (2006), others have refined this empirical analysis. Hamilton
(2008) argued that, since the CEX is notoriously noisy, one should trim the
sample to exclude outliers; this procedure leads to smaller rebate coefficients.
In Table I, we report the 2SLS estimate that is obtained by dropping the top and
bottom 05% and 15% of the distribution of nondurable consumption growth
from CEX. The rebate coefficient drops to a range of 22 to 24 percent, in
line with Hamilton’s results. Misra and Surico (2011) used quantile regression
techniques to explicitly deal with heterogeneity in the consumption responseCONSUMPTION RESPONSE TO FISCAL STIMULUS PAYMENTS 1207
TABLE I
ESTIMATES OF THE 2001 REBATE COEFFICIENT (β̂2 )a
Nondurables
JPS 2006, 2SLS (N = 13,066) 0375 (0136)
Trim top & bottom 0.5%, 2SLS (N = 12,935) 0237 (0093)
Trim top & bottom 1.5%, 2SLS (N = 12,679) 0219 (0079)
MS 2011, IVQR (N = 13,066) 0244 (0057)
a Nondurables include food (at home and away), utilities, household opera-
tions, public transportation and gas, personal care, alcohol and tobacco, miscel-
laneous goods, apparel good and services, reading materials, and out-of-pocket
health care expenditures. JPS 2006: Johnson, Parker, and Souleles (2006); MS
2011: Misra and Surico (2011). 2SLS: Two-Stage Least Squares; IVQR: Instru-
mental Variable Quantile Regression.
across households. Their point estimate was, again, around 0.24. Properly ac-
counting for outliers pushes the rebate coefficient toward the low end of the
original JPS estimates and, reassuringly, increases their precision. To facilitate
the comparison between model and data, it is useful to focus on one number,
and we take 025 as our preferred estimate.
Interpretation. It is crucial to understand the exact meaning of the rebate co-
efficient. The estimated coefficient β2 in equation (1) measures the consump-
tion growth for the treatment group (the rebate recipients at date t) relative
to consumption growth of the control group of non-recipients, with the com-
mon consumption growth component being subsumed by the time dummies.
The control group is composed of those who are already aware of the policy
but will receive the check at a later date, and those who have already received
the payment in the past. Thus, the consumption response of the control group,
which ideally should be unaffected by the policy, is, generally, a mix of the MPC
out of the news and the lagged MPC out of the payment. Thus, what exactly
does β2 measure?
To simplify the analysis, we split the population into two groups: early recipi-
ents (group A) who receive the check in 2001:Q2 and late recipients (group B)
g
who receive it in 2001:Q3. Let Δct be consumption growth of group g in quar-
ter t. Then, β2 is the average of (i) consumption growth of the treatment group
in Q2 (group A who receive the check in Q2) net of Q2 consumption growth of
the control group (group B who receive the check in Q3) and (ii) consumption
growth of the treatment group in Q3 (group B) net of Q3 consumption growth
of the control group (group A who receive the check in Q2), that is,
A
(ΔcQ2 − ΔcQ2
B
) + (ΔcQ3
B
− ΔcQ3
A
)
(2) β2 =
2
Consider now three alternative information structures: (i) the policy is an-
nounced in 2001:Q1, every consumer becomes aware of it at that date, and1208 G. KAPLAN AND G. L. VIOLANTE
TABLE II
ECONOMIC INTERPRETATION OF THE COMPONENTS OF THE REBATE COEFFICIENT β2 IN
EQUATION (2) UNDER THE THREE ALTERNATIVE INFORMATION STRUCTURES
Quarter 2 (Q2) Quarter 3 (Q3)
Group A Group B Group A Group B
Surprise for group A Δc to Δc to Lagged Δc to Δc to
surprise check news surprise check anticipated check
Anticipated by all Δc to 0 Lagged Δc to Δc to
anticipated check anticipated check anticipated check
Surprise for all Δc to 0 Lagged Δc to Δc to
surprise check surprise check surprise check
thus no consumer is surprised by the check upon receipt; (ii) the policy enters
agents’ information sets only when the check is actually received, and hence
every consumer is surprised by the arrival of the check; (iii) an intermediate
structure where the policy enters all agents’ information sets after the first
batch of checks is sent out (2001:Q2), that is, group A is surprised, but group
B is not. Table II describes the economic interpretation of each component
g
Δct under these three informational assumptions, when β2 is estimated as in
equation (1).
In the case where the policy is fully anticipated by all households, the rebate
coefficient β2 cannot be properly interpreted as an MPC out of the (antici-
pated) extra income because the consumption growth of the control group A
in Q3 incorporates the lagged reaction to the check received in Q2.12 For the
same reason, in the case where the policy is a surprise for all, β2 cannot be
interpreted as an MPC out of an unexpected income shock.13 Interestingly, in
both cases, one can fully take care of this problem by modifying the specifica-
tion of equation (1) as
(3) Δcit = β0s months + β1 Xit−1 + β2 Rit + β3 Rit−1 + εit
s
because the lag of the rebate variable absorbs the lagged consumption re-
sponse.14 In the intermediate information case, the interpretation of the re-
bate coefficient is further muddied by the fact that the consumption growth
12
The response of group B in Q2 is the lagged consumption response to the news received in
Q1. For unconstrained households it is zero, as they responded already in Q1, and for constrained
households it is also zero because they have not received the rebate yet.
13
In this case, one can infer the true MPC out of a surprise check from the consumption re-
sponse of the earliest recipients.
14
In JPS and PSJM, the baseline specification is equation (1). This augmented specification
with one or more lags was used by the authors to calculate the cumulative effect of the rebate
over several months.CONSUMPTION RESPONSE TO FISCAL STIMULUS PAYMENTS 1209
of the control group B in Q2 incorporates the reaction to the news, and thus
the addition of the lagged rebate in the regression does not fully resolve the
problem.
In spite of these difficulties in mapping directly β2 to an MPC, we maintain
that the rebate coefficient is an informative statistic: only if the true MPC out
of the check is sizable and the MPC out of the news is small, can the rebate co-
efficient be as large as is empirically estimated. The advantage of the structural
model is that it enables one to identify all the separate components of equation
(2). As a result, it allows one to quantify the current and lagged MPCs out of
an income shock, out of an anticipated income change, and out of the news of a
future change in income—all magnitudes that are essential for policy analysis.
3. A LIFE-CYCLE MODEL WITH LIQUID AND ILLIQUID ASSETS
Our framework integrates the Baumol–Tobin inventory-management model
of money demand into an incomplete-markets life-cycle economy. We first de-
scribe the full model; next, we use a series of examples to highlight the eco-
nomic mechanisms at work.
3.1. Model Description
Demographics. The stationary economy is populated by a continuum of
households, indexed by i. Age is indexed by j = 1 2 J. Households retire
at age J w and retirement lasts for J r periods.
Preferences. Households have an Epstein–Zin–Weil objective function de-
fined recursively by
1−σ 1−γ (1−σ)/(1−γ) 1/(1−σ)
(4) Vij = (1 − β) cijφ sij1−φ + β Ej Vij+1
where cij ≥ 0 is consumption of nondurables and sij ≥ 0 is the service flow from
housing for household i at age j. The parameter β is the discount factor, φ
measures the weight of nondurables relative to housing services in period-
utility, γ regulates risk aversion, and 1/σ is the elasticity of intertemporal sub-
stitution.15
Idiosyncratic Earnings. In any period during the working years, household
labor earnings (in logs) are given by
(5) log yij = χj + αi + zij
15
Piazzesi, Schneider, and Tuzel (2007) offered both (i) microevidence from CEX on the varia-
tion of housing expenditure share across different household types, and (ii) time-series evidence
on the relationship between the aggregate expenditure share and the relative price of housing
services. Both dimensions of the data suggest an elasticity of substitution between nondurable
and housing consumption very close to 1, which is the Cobb–Douglas case that we adopt in our
preference specification.1210 G. KAPLAN AND G. L. VIOLANTE
where χj is a deterministic age profile common across all households, αi is a
household-specific fixed effect, and zij is a stochastic idiosyncratic component
that obeys the conditional c.d.f. Γ z (zj+1 zj ).
Assets. Households can hold a liquid asset mij and an illiquid asset aij . The
illiquid asset pays a gross financial return 1/qa , whereas positive balances of
the liquid asset pay 1/qm . When the household wants to make deposits into,
or withdrawals from, the illiquid account, it must pay a transaction cost κ.16
The trade-off between these two savings instruments is that the illiquid asset
earns a higher return, in the form of capital gain and consumption flow, but its
adjustments are subject to the transaction cost. Households start their working
lives with an exogenously given quantity of each asset.
Illiquid assets are restricted to be always nonnegative, aij ≥ 0. Because of the
prevalence of housing among commonly held illiquid assets (see Section 5),
we let the stock of illiquid assets aij yield a utility flow with proportionality
parameter ζ > 0. Households are also free to purchase or rent out housing
services hij ≥ −ζaij on the market.17 As a result, sij = ζaij + hij .
We allow borrowing in the liquid asset to reflect the availability of unsecured
credit up to an ad hoc limit, mj+1 (yij ), expressed as a function of current labor
earnings. The interest rate on borrowing is denoted by 1/q̄m and we define
the function qm (mij+1 ) to encompass both the case mij+1 ≥ 0 and the case
mij+1 < 0.
Financial returns to the liquid and illiquid assets, as well as the borrowing
rate, are exogenous. Two reasons dictate the choice of abstracting from the
equilibrium determination of returns. First, the total outlays from the 2001 re-
bate amounted to less than 0.1% of aggregate net worth, surely not enough to
move asset prices significantly. Second, 83% of aggregate wealth is held by the
top quintile of the distribution (Díaz-Giménez, Glover, and Ríos-Rull (2011,
Table 6)), and the portfolio allocation of such households is unlikely to be af-
fected by the receipt of a $500 check from the government.18
Government. Government expenditures G are not valued by households.
Retirees receive social security benefits p(χJ w αi ziJ w ), where the arguments
proxy for average gross lifetime earnings. The government levies proportional
taxes on consumption expenditures (τc ) and on asset income (τa τm ), a payroll
tax τss (yij ) with an earnings cap, and a progressive tax on labor income τy (yij ).
There is no deduction for interest paid on unsecured borrowing. We denote
16
It is straightforward to allow for a utility cost or a time cost proportional to labor income
rather than a monetary cost of adjustment. We have experimented with both types of costs and
obtained similar results in both cases. See Kaplan and Violante (2011).
17
This assumption adds realism to the model. Technically, it is useful because, with our Cobb–
Douglas period-utility specification, housing services are an essential consumption good and,
without a rental market, even the poorest households would be forced to pay the transaction
cost in order to deposit into the illiquid account to start enjoying a minimum amount of housing
services.
18
In simulations, the aggregate stock of illiquid wealth increases by only 0.14% during the first
year of the transition, an amount hardly large enough to have an impact on the rate of return.CONSUMPTION RESPONSE TO FISCAL STIMULUS PAYMENTS 1211
the combined income tax liability function as T (yij aij mij ). For retirees, the
same tax function applies with yij taking the value p(·). Finally, we let the gov-
ernment issue one-period debt B at price qg .
Household Problem. We use a recursive formulation of the problem. Let sj =
(mj aj α zj ) be the vector of individual states at age j. The value function of a
household at age j is Vj (sj ) = max{Vj0 (sj ) Vj1 (sj )}, where Vj0 (sj ) and Vj1 (sj ) are
the value functions conditional on not adjusting and adjusting (i.e., depositing
into or withdrawing from) the illiquid account, respectively. This decision takes
place at the beginning of the period, after receiving the current endowment
shock, but before consuming.19
Consider a household of age j. If Vj0 (sj ) ≥ Vj1 (sj ), the household chooses
not to adjust its illiquid assets and solves the dynamic problem
1−σ 1−γ (1−σ)/(1−γ) 1/(1−σ)
(6) Vj0 (sj ) = max (1 − β) cjφ sj1−φ + β Ej Vj+1
cj hj mj+1
subject to:
1 + τc (cj + hj ) + qm (mj+1 )mj+1 = yj + mj − T (yj aj mj )
sj = hj + ζaj
qa aj+1 = aj
cj ≥ 0 hj ≥ −ζaj mj+1 ≥ −mj+1 (yj )
exp(χj + α + zj ) if j ≤ J w
yj =
p(χJ w α zJ w ) otherwise
where zj evolves according to the conditional c.d.f. Γjz .
If Vj0 (sj ) < Vj1 (sj ), the household adjusts its holding of illiquid assets and
solves
1−σ
(7) Vj1 (sj ) = max (1 − β) cjφ sj1−φ
cj hj mj+1 aj+1
1−γ (1−σ)/(1−γ) 1/(1−σ)
+ β Ej Vj+1
subject to:
1 + τc (cj + hj ) + qm (mj+1 )mj+1 + qa aj+1
= yj + mj + aj − κ − T (yj aj mj )
19
Because of this timing, after the earnings shock the household can always choose to pay the
transaction cost, access the illiquid account, and use all its resources to finance consumption.
Hence, our model does not feature a cash-in-advance (CIA) constraint. See Jovanovic (1982) for
an exhaustive discussion of the difference between models with transaction costs and models with
CIA constraints.1212 G. KAPLAN AND G. L. VIOLANTE
sj = hj + ζaj
cj ≥ 0 hj ≥ −ζaj mj+1 ≥ −mj+1 (yj ) aj+1 ≥ 0
exp(χj + α + zj ) if j ≤ J w
yj =
p(χJ w α zJ w ) otherwise
Appendix E in Supplemental Material (Kaplan and Violante (2014)) describes
the computational algorithm used to solve problems (6) and (7).
Balanced Budget. The government always respects its intertemporal budget
constraint
J
1
(8) G+ p(yJ w ) dμj + −1 B
j=J w +1
qg
J
J
= τc cj dμj + T (yj aj mj ) dμj
j=1 j=1
where μj is the distribution of households of age j over the individual state
vector sj .
4. HAND-TO-MOUTH HOUSEHOLDS IN MODEL AND DATA
In this section, we first illustrate, by means of numerical examples, how hand-
to-mouth behavior arises endogenously in our model, even when agents hold
positive illiquid wealth. Next, we measure hand-to-mouth households in the
Survey of Consumer Finances.
4.1. Behavior in the Model: The “Wealthy Hand-to-Mouth”
For ease of exposition, we focus on a stylized version of the model with time-
separable preferences (γ = σ), without service flow from illiquid assets (φ = 1,
ζ = 0), with logarithmic period-utility, deterministic labor income (zj = 0), and
no taxes ( T (·) = τc = 0). Moreover, we assume that q̄m < qa < qm . The sec-
ond inequality states that the illiquid asset has a higher return and the first
one ensures that households do not borrow to deposit into the illiquid ac-
count.
Two Euler Equations. Consumption and portfolio decisions are character-
ized by a short-run Euler equation (EE-SR) that corresponds to borrowing or
saving in the liquid asset, and a long-run Euler equation that corresponds to
(dis)saving in the illiquid asset (EE-LR). In periods where the working house-CONSUMPTION RESPONSE TO FISCAL STIMULUS PAYMENTS 1213
hold does not adjust,
β
(EE-SR) u (cj ) = u (cj+1 )
qm (mj+1 )
The slope of her consumption path is governed by β/qm (mj+1 ). For plausible
parameterizations, when the household is in debt (mj+1 < 0), this ratio is above
1: the consumption path is increasing as the household saves her way out of ex-
pensive borrowing. When the household is saving (mj+1 > 0), this ratio is below
1: consumption declines over time because of impatience and the low real re-
turn on cash. There are two kinks in the budget constraints where equation
(EE-SR) does not hold: mj+1 = −mj+1 (yj ), the debt limit, and mj+1 = 0, be-
cause of the wedge between the return on liquid saving and the interest on un-
secured credit (q̄m < qm ). Households on the kinks are hand-to-mouth, mean-
ing that they consume all their income.
During the working life, an agent will eventually want to save to finance
consumption in retirement by making deposits into the illiquid account. Given
the fixed cost of adjusting, households accumulate liquid funds and choose
infrequent dates at which to add some or all of their liquid holdings to the
illiquid asset (the “cake-baking” problem). Across two such adjustment dates
N periods apart, consumption dynamics are dictated by
N
β
(EE-LR) u (cj ) = u (cj+N )
qa
Since β/qa > β/qm , consumption grows more (or falls less) across adjustment
dates than between adjustments.
During retirement, the household faces a cake-eating problem, where opti-
mal decisions closely resemble those in Romer (1986). Consumption in excess
of pension income is financed by making periodic withdrawals from the illiquid
account. Between each withdrawal, the household runs down its liquid hold-
ings and consumption falls according to (EE-SR). The withdrawals are timed
to coincide with the period where cash is exhausted. Equation (EE-LR) holds
across withdrawals.
Poor Hand-to-Mouth Behavior. Figure 1 shows consumption and wealth dy-
namics in an example where an agent starts her working life with zero wealth,
receives an increasing endowment while working, and a constant endowment
when retired. To make this example as stark as possible, we impose a very large
transaction cost. Panel (a) shows that, because of the increasing earnings pro-
file, the agent in this example chooses first to borrow to smooth consumption,
and then starts saving for retirement. She adjusts her illiquid account at only
three points in time: one deposit while working, after repaying her debt, and1214 G. KAPLAN AND G. L. VIOLANTE
FIGURE 1.—Example of life-cycle of a poor hand-to-mouth agent in the model.
two withdrawals in retirement. After its inception, the value of the illiquid ac-
count grows at rate 1/qa .20
Panel (b) shows her associated earnings and consumption paths. In the same
panel, we have also plotted the paths for consumption arising in the two ver-
sions of the corresponding one-asset model: one with the short-run interest
rate 1/qm (mj+1 ), and one with the long-run rate 1/qa . The sawed pattern for
consumption that arises in the two-asset model is a combination of the short-
run and long-run behavior: between adjustment dates, the consumption path
is parallel to the path in the one-asset model with the low return; while across
adjustment dates, the slope is parallel to consumption in the one-asset model
with the high return. Finally note that, after repayments of her debts, this agent
is poor hand-to-mouth. In other words, she keeps zero net worth and consumes
all her income for a phase of her life, before starting to save.
Wealthy Hand-to-Mouth Behavior. Figure 2 illustrates how the model can fea-
ture households with positive net worth who consume their income every pe-
riod: the wealthy hand-to-mouth agents. The parameterization is the same as
in Figure 1, except for a higher return on the illiquid asset. This higher return
leads to stronger overall wealth accumulation, but rather than increasing the
number of deposits during its working life, the household changes the timing
of its single deposit: the deposit into the illiquid account is now made earlier
in life in order to take advantage of the high return for a longer period (com-
pare the left panels across Figures 1 and 2). Thus, the household optimally
20
Over the working life, the household piles up liquid funds in anticipation of her deposit into
the liquid account, but also to smooth consumption across her transition into retirement. As we
show in Appendix C.4, this pattern of accumulation of liquid wealth around retirement survives
in the richer model with heterogeneity and uncertainty and is also distinctly visible in the micro
data.CONSUMPTION RESPONSE TO FISCAL STIMULUS PAYMENTS 1215
FIGURE 2.—Example of life-cycle of a wealthy hand-to-mouth agent in the model.
chooses to hold zero liquid assets in the middle of the working life, after her
deposit, while the illiquid asset holdings are positive and are growing in value.
Intuitively, since her net worth is large, this household would like to consume
more than her earnings flow, but the transaction cost and the high interest rate
on unsecured borrowing dissuade her from doing so. This is a household that,
upon receiving the rebate, will consume a large part of it and, upon the news
of the rebate, will not increase her expenditures.
Why would households choose to consume all of their earnings and deviate
from the optimal consumption path imposed by the short-run Euler equation
(EE-SR), even for long periods of time? The answer is that households are
better off taking this welfare loss because avoiding it entails either (i) paying
the transaction cost more often to withdraw cash in order to consume more
than income; (ii) holding larger balances of liquid wealth and hence forego-
ing the high return on the illiquid asset (and, therefore, the associated higher
level of long-run consumption); or (iii) using expensive unsecured credit to
finance expenditures.21 We note that this logic is reminiscent of Cochrane’s
(1989) insight that the utility loss from setting consumption equal to income
is second-order in a representative agent model with reasonable risk aversion
and income volatility. Browning and Crossley (2001) reported similar calcula-
tions in the context of a life-cycle one-asset model of consumption and sav-
ing.
21
While we have focused our examples on poor and wealthy hand-to-mouth behavior at the
kink for zero liquid wealth, there is a second type of hand-to-mouth behavior when agents borrow
up to the credit limit. This limit is the second kink in the budget constraint. In this case, option
(iii) is obviously not feasible. In Appendix A, we illustrate an example of wealthy hand-to-mouth
behavior at the credit limit.1216 G. KAPLAN AND G. L. VIOLANTE
4.2. The SCF Data
We begin with some descriptive statistics about household portfolios in the
Survey of Consumer Finances (SCF). We then explain how we exploit these
data to estimate the proportion of hand-to-mouth households in the United
States.
Households’ Portfolio Data. Our data source is the 2001 wave of the SCF,
a triennial cross-sectional survey of the assets and debts of U.S. households.
For comparability with the CEX sample in JPS (2006), we exclude the top 5%
of households by net worth. Average (median) labor income for the working-
age population is $52,745 ($41,000), a number close to the one reported by JPS
(2006, Table 1).22 Our definition of liquid assets comprises: cash, money market
(MM), checking, savings, and call accounts as well as directly held mutual funds
(MF), stocks, bonds, and T-Bills net of revolving debt on credit card balances.
In Appendix B.1, we describe our identification of revolving debt and our cash
imputation procedure, needed because the SCF does not record household
cash holdings.23
Our baseline measure of illiquid assets includes housing net of mortgages
and home equity loans, retirement accounts (e.g., IRA, 401K), life insurance
policies, CDs, and saving bonds. Table III reports some descriptive statistics.
As expected, the bulk of household wealth is held in illiquid assets, notably
housing and retirement accounts. For example, the median of the liquid and
illiquid asset distributions are $2,629 and $54,600, respectively. Moreover, over
their working life, households save disproportionately through illiquid wealth
and keep holdings of liquid wealth fairly stable: median illiquid assets grow
by around $100,000 from age 30 to retirement, whereas median liquid wealth
increases by less than $5,000.
Measurement of Hand-to-Mouth Households. In the model, we define a
household to be hand-to-mouth (hereafter, HtM) if it chooses to be at one
of the kinks of her budget constraint, either zero liquid wealth or the credit
limit. Such a household will have a high marginal propensity to consume out of
an extra dollar of windfall income. How can we identify these HtM households
in the SCF data?
To measure HtM households at the zero kink for liquid wealth, we start from
the observation that, since these households do not borrow and do not save
through liquid assets, they do not carry any liquid wealth across pay-periods.
If we observed liquid balances at the end of the period in the data, we could
22
In our definition of household labor income, we include unemployment and disability insur-
ance, TANF, and child benefits.
23
Briefly, our cash imputation uses data from the Survey of Consumer Payment Choice ad-
ministered by the Federal Reserve Bank of Boston. To calculate revolving unsecured debt, we
use a combination of different SCF questions. This strategy, which is common in the literature
(see Telyukova (2013)), avoids including purchases made through credit cards in between regular
payments as debt.CONSUMPTION RESPONSE TO FISCAL STIMULUS PAYMENTS 1217
TABLE III
HOUSEHOLD PORTFOLIO COMPOSITIONa
Median Mean Fraction Return
($2001) ($2001) Positive (%)
Earnings plus benefits (age 22–59) 41,000 52,745 – –
Net worth 62,442 150,411 0.90 17
Net liquid wealth 2,629 31,001 0.77 −15
Cash, checking, saving, MM accounts 2,858 12,642 0.92 −22
Directly held MF, stocks, bonds, T-Bills 0 19,920 0.29 17
Revolving credit card debt 0 1,575 0.41 –
Net illiquid wealth 54,600 119,409 0.93 23
Housing net of mortgages 31,000 72,592 0.68 20
Retirement accounts 950 34,455 0.53 35
Life insurance 0 7,740 0.27 01
Certificates of deposit 0 3,807 0.14 09
Saving bonds 0 815 0.17 01
a Authors’ calculations based on the 2001 Survey of Consumer Finances (SCF). The return reported in the last col-
umn is the real after-tax risk-adjusted return. MM: money market; MF: mutual funds. See Appendix B.1 for additional
details.
easily identify these HtM agents, but the SCF reports only the average liquid
balance during the last month. Average balances are positive for all house-
holds (HtM and not) because labor income is paid as liquid assets and because
of a mismatch in the timing of consumption and earnings within a pay-period.
Then, a strict criterion to identify these HtM agents in the data is to count
those households in the SCF whose average balance of liquid wealth is equal
to or less than half their earnings per pay-period. (The “half” presumes re-
sources being consumed at a constant rate.)24 Symmetrically, we measure HtM
agents at the credit limit as those SCF households with negative holdings of
liquid wealth that are lower than half their pay-period earnings minus their
self-reported total credit limit.
Any sample split based on income and liquid wealth is bound to contain
both type I and type II classification error (see, e.g., Jappelli (1990)). Never-
theless, our estimate is likely to be a lower bound because, while all non HtM
households would always hold average liquid balances above half their earn-
ings, some HtM households at the zero kink may fall in this latter group as
well.25
24
Alvarez and Lippi (2009) suggested this calculation as a test of the liquidity management
model.
25
If the household starts the period with some savings in addition to earnings and ends the
period with some savings, its average balance would be above half earnings. If its initial balance
equals only earnings for that period and it ends the period with positive savings, the average
balance would also be above half earnings. Neither of these households is HtM. However, if1218 G. KAPLAN AND G. L. VIOLANTE
The examples in Section 4.1 show that there are two types of HtM agents.
There are poor HtM agents without any illiquid assets, and wealthy HtM
agents who have positive balances of illiquid wealth. In the SCF, we identify
wealthy HtM agents as those households who satisfy the HtM requirements
listed above and, at the same time, hold illiquid assets.
Appendix B.2 contains more details on this measurement. There, we also
perform a robustness analysis with respect to the frequency of the pay-period
(weekly, bi-weekly, monthly), the definition of liquid wealth (whether it only
includes cash and bank accounts or also directly held stocks and bonds) and
the definition of illiquid wealth (whether it also includes vehicles), and the
definition of wealthy HtM (whether the HtM household holds at least $3,000
in its illiquid account, which is the median amount of liquid wealth).
Our estimates imply that between 17.5% and 35% of households are HtM
in the United States. Among these, between 40 and 80 percent are wealthy
HtM, depending mainly on the pay frequency and on whether one expands
the notion of illiquid wealth by including vehicles. This group of wealthy HtM
households, which represents a sizable fraction of the population (between 7%
and 26%), is only visible through the lens of the two-asset model. From the dis-
torted point of view of the standard one-asset model, these are households with
positive net worth, and are hence unconstrained. It is useful to compare these
estimates with those that one would obtain when HtM agents are measured in
terms of net worth.26 We compute that between 4% and 14% of U.S. house-
holds are HtM in terms of net worth, depending largely on whether vehicles
are considered part of wealth.
Because of the lower bound nature of our estimator, in the model we target
a total fraction of HtM households on the high end of the range, around 1/3
of the population. This target is also consistent with three additional pieces
of survey evidence. First, the SCF asks households whether “in the past year
their spending exceeded their income, but did not spend on a new house, a new
vehicle, or on any investment.” Almost 36% of households fall into this cate-
gory. Second, Lusardi, Schneider, and Tufano (2011) documented that around
1/3 of U.S. households would “certainly be unable to cope with a financial
emergency that required them to come up with $2,000 in the next month.” The
authors also reported that, among those giving that answer, a high proportion
of individuals are at middle class levels of income. Similarly, Broda and Parker
(2012) documented, from the AC Nielsen Homescan database, that 40% of
households report that they do not have “at least two months of income avail-
able in cash, bank accounts, or easily accessible funds.”
a household starts the period with positive savings in addition to earnings and ends the period
with zero liquid savings, its average liquid balance would be above half earnings, but she is a HtM
household in that period.
26
We define HtM households in terms of net worth in the same way. A household is HtM
(in terms of net worth) if it has (i) positive net worth below half its earnings per pay-period, or
(ii) negative net worth lower than half its earnings minus its credit limit.You can also read
